I have difficulty understanding why any discussion of taxes in the US becomes a conversation about the income tax. There are many, many taxes in the US. A rational discussion of taxes would include all of the taxes together. Most states have a sales tax, and the tax is regressive. Several states (North Carolina, Alabama and many others) make the sales tax much more regressive by putting a cap on it. I recall, when I lived in North Carolina during the 90s, the sales tax had a cap at $100. So the kind of everyday items that poor people have to buy would face the full tax, but plenty of consumer goods that the middle class bought (lots of consumer electronics, for instance) did not face the full tax since the items cost over $100. In essence, the poor were the only ones who had to the full sales tax on nearly everything they bought.

In almost all 50 states, the overall tax code is regressive - the middle classes are taxed more heavily than the rich. The regressive nature of the state taxes is offset by the progressive nature of the Federal taxes.

Imagine re-doing the above scenario of 10 men in a bar, but doing it in an accurate way, where there is sales tax on those beers - then the story comes out rather differently.